Question: $g(x) = x^{2}-2x$ $h(n) = 2n^{2}-6n-3+3(g(n))$ $f(x) = 4x-2(g(x))$ $ f(h(2)) = {?} $
Explanation: First, let's solve for the value of the inner function, $h(2)$ . Then we'll know what to plug into the outer function. $h(2) = 2(2^{2})+(-6)(2)-3+3(g(2))$ To solve for the value of $h$ , we need to solve for the value of $g(2)$ $g(2) = 2^{2}+(-2)(2)$ $g(2) = 0$ That means $h(2) = 2(2^{2})+(-6)(2)-3+(3)(0)$ $h(2) = -7$ Now we know that $h(2) = -7$ . Let's solve for $f(h(2))$ , which is $f(-7)$ $f(-7) = (4)(-7)-2(g(-7))$ To solve for the value of $f$ , we need to solve for the value of $g(-7)$ $g(-7) = (-7)^{2}+(-2)(-7)$ $g(-7) = 63$ That means $f(-7) = (4)(-7)+(-2)(63)$ $f(-7) = -154$